Cochran's Theorem is a statistical principle that provides a way to analyze the variance of a set of random variables. It states that if you have a linear combination of independent random variables, the variance of that combination can be expressed in terms of the variances of the individual variables. This theorem is particularly useful in the field of analysis of variance (ANOVA), where it helps in understanding how different factors contribute to the overall variability in data. The theorem is named after William G. Cochran, a prominent statistician who made significant contributions to the field of statistics. By applying Cochran's Theorem, researchers can simplify complex statistical models and make more accurate inferences about their data. This makes it an essential tool in experimental design and data analysis.